How to make a popup Menu in the BGE?
Have your first button in the game trigger a new object (lets call it menu2) to be added to the game, or play a animation to move menu2 on screen. Then on menu2 have several other objects parented to the menu, each with logic set up like in this question.

In the blend file you will find the object menu2 has a animation to move it in to view. That animation is triggered by the first button (a cube). The trick to playing the animation is to have the Action Actuator on the menu. The logic bricks look like this.

So every time there is a click on the cube it triggers the animation to play on the menu. You can have logic bricks go between objects, just select both objects and they will show up on the logic brick editor.

BGE menu demo blend file.